PORTUGALIAEMATHEMATICA
Vol. 62, No. 3, pp. 247-268 (2005)
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PORTUGALIAE MATHEMATICA Vol. 62, No. 3, pp. 247-268 (2005) |
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On bi-Lipschitz embeddingsH. Movahedi-Lankarani and R. WellsDepartment of Mathematics and Statistics, Penn State Altoona,Altoona, PA 16601-3760 -- USA E-mail: hml@math.psu.edu Department of Mathematics, Penn State University, University Park, PA 16802 -- USA E-mail: wells@math.psu.edu Abstract: Let $\mu$ be a finite Borel regular measure on a compact metric space $(X,\rho)$, nontrivial on nonempty open sets. It is shown that whenever the map $\iota_{\rho}: X\to L^p(\mu)$ given by $\iota_{\rho}(x)=\rho(x,\cdot)$ is lower Lipschitz for some $1<p<\infty$, then there is a bi-Lipschitz embedding of $(X,\rho)$ into some $\R^N$. Keywords: Lipschitz; bilipschitz; bi-Lipschitz; embedding; spherically compact; canonical map; evaluation map. Classification (MSC2000): 54E40, 58C20.; 54C25, 54F45, 54F50, 58C25, 57R35, 57R40, 26B05. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2005 Sociedade Portuguesa de Matemática
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